Publications related to Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...

2020

Markov cubature rules for polynomial processes

Damir Filipovic, Martin Larsson, Sergio Andres Pulido Nino

We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rul ...

ELSEVIER2020

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of agents) relative to no ...

IEEE2020

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sen ...

IEEE2019

Distributed Learning over Networks under Subspace Constraints

Ali H. Sayed, Stefan Vlaski, Roula Nassif

This work presents and studies a distributed algorithm for solving optimization problems over networks where agents have individual costs to minimize subject to subspace constraints that require the minimizers across the network to lie in a low-dimensional ...

IEEE2019

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

Mean-Field methods for Structured Deep-Learning in Computer Vision

Pierre Bruno Baqué

In recent years, Machine Learning based Computer Vision techniques made impressive progress. These algorithms proved particularly efficient for image classification or detection of isolated objects. From a probabilistic perspective, these methods can predi ...

EPFL2018

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Martin Vetterli, Arash Amini, Mitra Fatemi

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

\mathds{1}_{\{p\leq0\}}

to the image plane, where

\mathds{1}

denotes the indicator function and

p

is some r ...

2016

Stochastic Spectral Descent for Restricted Boltzmann Machines.

Volkan Cevher

Restricted Boltzmann Machines (RBMs) are widely used as building blocks for deep learning models. Learning typically proceeds by using stochastic gradient descent, and the gradients are estimated with sampling methods. However, the gradient estimation is a ...

2015

TCHo: A Code-Based Cryptosystem

Serge Vaudenay, Alexandre Raphaël Duc

TCHo is a public-key cryptosystem based on the hardness of finding a multiple polynomial with low weight and on the hardness of distinguishing between the output of an LFSR with noise and some random source. An early version was proposed in 2006 by Finiasz ...

Springer Berlin Heidelberg2013

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

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Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Markov cubature rules for polynomial processes

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Distributed Learning over Networks under Subspace Constraints

Four-Variable Expanders Over The Prime Fields

Mean-Field methods for Structured Deep-Learning in Computer Vision

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Stochastic Spectral Descent for Restricted Boltzmann Machines.

TCHo: A Code-Based Cryptosystem

Distributed Learning over Networks under Subspace Constraints

TCHo: A Code-Based Cryptosystem

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Four-Variable Expanders Over The Prime Fields

Markov cubature rules for polynomial processes

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Polynomial Escape-Time From Saddle Points In Distributed Non-Convex Optimization

Linear Speedup In Saddle-Point Escape For Decentralized Non-Convex Optimization

Mean-Field methods for Structured Deep-Learning in Computer Vision

Stochastic Spectral Descent for Restricted Boltzmann Machines.